The mammalian circadian clock is a cell-autonomous system that drives oscillations in behavior and physiology in anticipation of daily environmental change. To assess the robustness of a human molecular clock, we systematically depleted known clock components and observed that circadian oscillations are maintained over a wide range of disruptions. We developed a novel strategy termed Gene Dosage Network Analysis (GDNA) in which small interfering RNA (siRNA)-induced dose-dependent changes in gene expression were used to build gene association networks consistent with known biochemical constraints. The use of multiple doses powered the analysis to uncover several novel network features of the circadian clock, including proportional responses and signal propagation through interacting genetic modules. We also observed several examples where a gene is up-regulated following knockdown of its paralog, suggesting the clock network utilizes active compensatory mechanisms rather than simple redundancy to confer robustness and maintain function. We propose that these network features act in concert as a genetic buffering system to maintain clock function in the face of genetic and environmental perturbation.